Evaluate: `("lim")_(x→0,y→0)(y^2+sinx)/(x^2+siny^2)` where `(x , y)→(0,0)` along the curve `x=y^2`

Evaluate lim_(yto0)(y^(2)+sin x)/(x^(2)+siny^(2)), where (x,y)to(0,0) along the curve x=y^(2) .

Evaluate: lim_((x,y)->(0,0))(x^(3)y)/(x^(4)+y^(4))

The value of lim_(x->1) y^3/(x^3-y^2-1) as (x, y)-> (1, 0) along the line y = x -1 is

The value of lim_(x->1) y^3/(x^3-y^2-1) as (x, y)-> (1, 0) along the line y = x -1 is

A curve satisfies the differential equation (dy)/(dx)=(x+1-xy^2)/(x^2y-y) and passes through (0,0) (1) The equation of the curve is x^2+y^2+2x=x^2y^2 (2) The equation of the curve is x^2+y^2+2x+2y=x^2y^2 (3) x=0 is a tangent to curve (4) y=0 is a tangent to curve

Find the area enclosed with in the curve x=2-5y-3y^(2), x=0

Find the area enclosed with in the curve x^(2)=4y,x=2, y=0

Find the asymptotes of the curve x y-3y-2x=0 .

lim_(xto0) [min(y^(2)-4y+11)(sinx)/(x)] (where [.] denotes the greatest integer function) is

Find the area bounded by the curves x+2|y|=1 and x=0 .